MathDB

Easier version of Tuymaada seniors P7

Source: Tuymaada 2024 Juniors P7

July 10, 2024

algebraPolynomials

Problem Statement

Given are quadratic trinomials

f

and

g

with integral coefficients. For each positive integer

n

there is an integer

k

such that

\frac{f(k)}{g(k)}=\frac{n + 1}{n}.

Prove that

f

and

g

have a common root. Proposed by A. Golovanov